`tril`

Lower triangular part of a matrix.

Syntax

L = tril(A)

Keeps the main diagonal and everything below it; the rest becomes zero.

L = tril(A, k)

Keeps the elements on and below the k-th diagonal.

Description

tril(A) zeroes the elements above the main diagonal. With k = -1 the diagonal is removed as well, giving the strictly lower part, so A = tril(A,-1) + diag(diag(A)) + triu(A,1).

It is handy for building triangular systems and for extracting the part of a symmetric matrix that is stored once.

Input arguments

A: Matrix (any class).
k: Integer diagonal offset: 0 is the main diagonal, positive values are above it, negative values below. Default 0.

Output arguments

L: Matrix of the same size and class as A.

Example

Lower part with offsets

A = magic(3);
tril(A)
tril(A, -1)

Output

ans = 3×3

     8     0     0
     3     5     0
     4     9     2
ans = 3×3

     0     0     0
     3     0     0
     4     9     0

tril